Evaluate the following as true or false In order to change t

Evaluate the following as true or false. In order to change the homogeneous differential equation dy/dx - f(x, y) to dy/dx = g(y/x) form. It is necessary to divide each term of f(x, y) by the highest power of x present in f(x, y). Select one: True False

Solution

Solution : It is false. It is not necessary to divide each term of f(x , y) by

the higest power of x present in the f(x , y).

For Example :

dy/dx = (x^2 + y^2)/(xy)

Start with : (x^2 + y^2)/(xy)

Separate the terms : we get (x^2)/(xy) + (y^2)/(xy)

Simplify , we get : (x/y) + (y/x)

Reciprocal of first term : (y/x)^-1 + (y/x)

So we get, dy/dx = (y/x)^-1 + (y/x)

Here in the original equation dy/dx = (x^2 + y^2)/(xy) , the degree of x is 2, but here we divide by x not x^2.